Question

In 2005, Dashrath's age was 11 times as
that of his son. In 2020, his age becomes
14 times as that of his son's age in 2005.
By how many years was Dashrath elder to
his son in 2005?
(A) 30 years
(C) 25 years
(B) 50 years
(D) 5 years​

Answer 1

Answer:

50 years

Step-by-step explanation:

In 2005 let sons age = x

in 2005 Dashrath's age becomes= 11x

In 2020 i.e; after 15 years dashrath's age becoms = 11x + 15

Now, given that dashraths age in 2020 becomes 14 times that of his son

i.e; 11x + 15 =  14x

      15 = 3x

       x = 5

Therefore sons age in 2005 was = 5 years

Therefore dashrath;s age in 2005 was = 55 years

Now dashrat is elder to his son 2005 by = 55 - 5

                                                                    = 50 years

Answer 2

Dashrath was 50 years older than his son in 2005.

Option 'B' is correct.

Given:

• In 2005, Dashrath's age was 11 times that of his son.
• In 2020, his age will be 14 times as that of his son's age in 2005.

To find:

• How many years was Dashrath elder to his son in 2005?
• (A) 30 years
• (B) 50 years
• (C) 25 years
• (D) 5 years

Solution:

Step 1:

Write equations.

Let Dashrath's age in 2020 be 'x' years and his son age be 'y' years.

In 2005 his age was (x-15) years.

and his son in 2005 was (y-15) years,

ATQ,

In 2005, Dashrath's age was 11 times as

that of his son;

$(x - 15) = 11(y - 15)$

or

$x - 15 = 11y - 165$

$\bf x - 11y = - 150...eq1$

In 2020,his age will be 14 times as that of his son's age in 2005.

$x = 14(y - 15)$

$\bf x - 14y = - 210...eq2$

Step 2:

Solve both equations.

Solve eq1 and eq2 to find the values of x and y.

eq1-eq2

$x - 11y = - 150 \\ x - 14y = - 210 \\ ( - ) \: \: \: ( + ) \: \: \: \: ( + ) \: \: \: \: \: \\ - - - - - - - - \\3y = 60$

$\bf y = 20$

The age of Dashrath's son is 20 years in 2020.

Put value of y in eq1.

$x - 11 \times 20 = - 150$

$x - 220 = - 150$

$x = - 150 + 220$

$\bf x = 70$

The age of Dashrath is 70 years in 2020.

Difference of age between father and son will equal, either consider 2005 or consider 2020.

Thus,

Difference between both ages is 50 years in 2005.

Option 'B' is correct.

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